Poincaré bifurcations in polynomial differential systems (Q2721869)

The author considers Poincaré bifurcations for polynomial differential systems. Usually Pontryagin's method of perturbed Hamiltonian systems is used to deal with such problems by studying the number and multiplicity of zeros for certain Abelian integrals. Many results have been given for concrete polynomial systems applying this method. NEWLINENEWLINENEWLINEHowever, since the method is inapplicable to the case where the perturbed system has a complicated Hamiltonian function or the system is integrable but non-Hamiltonian, the author suggests another approach to avoid complicated calculations of the Abelian integrals. He studies the Poincaré bifurcation starting from the Hopf bifurcations of all possible orders and gives a complete result for the Poincaré bifurcations in quadratic systems of Bautin's form.